This thesis explores the vibrational behavior of the main components of sound production in the violin using a continuum mechanics approach. The author provides a mathematical description of the regions in the vibrating continuum, and begins to develop a system of equations governing their behavior, focusing on the air in...
The goal of this research project is to determine the fractal nature, if any, which
certain surface water waves exhibit when viewed on a microscopic scale. We make
use of the mathematical formulation of non-viscous fluids describing their physical
properties. Using these expressions and including boundary conditions for free
surfaces...
This is an interactive, self explanatory computer
program on real roots of polynomials with real
coefficients. This program called POLYROOT has the double
feature of tutoring and problem solving. It allows the user
to enter on one line any polynomial with real coefficients.
Then, the user can find :
1....
Two numerical methods are presented that can be used to solve
second order nonlinear ordinary differential equations with periodic
boundary conditions. One of these methods is a shooting method developed
solely for the periodic problem. The other, "quasilinearization,"
is a method applicable to a wide variety of problems. It is...
We investigate in this thesis, the problem of stability
of thermo-viscoelastic fluid flow between rotating
coaxial cylinders. By using the thermo-viscoelastic
constitutive equations given by Eringen, we reduce the
equations of motion into a form suitable for stability
analysis. The course of reduction which we follow yields
some interesting intermediate...
This thesis documents a new language which facilitates
the construction of Turing machines. The language translator
is written in Compass and has been debugged and is
available for use on the CDC 3300.
This paper defines four function space topologies,
characterizes two of them in terms of more familiar
concepts, and compares the four topologies. Then in the
cases of the two less familiar topologies we have considered
several common properties of topological spaces
and attempted to answer the following question: If the...
By various experiments, it has been found that the response
of real materials to external forces is, in general,
nonlinear in character. In classical continuum mechanics,
the use of ordinary measures of strain have forced the
constitutive equations to take complex forms and since the
orders of these measures are...
The study of water movement in unsaturated soils by using appropriate
diffusion equations has attracted considerable attention in
recent years.
In this study, a numerical technique is developed for solving
a generalized, dimensionless diffusion equation by the use of a digital.
computer. Diffusivity and capillary conductivity equations derived
by Brooks...
The system of partial differential equations which governs the
motion of a Newtonian fluid has been known for over a century. Yet,
due to the complexity of the equations, an analytical solution is known
only for a few simple geometries or a few special cases such as very
slow motion....
Consider a transformation group G operating on a space X
and a G- invariant function f defined on a G- invariant subset of
X. By imposing suitable conditions on X, G, f and A, the
author derives sufficient conditions for extending f invariantly to
the whole space, and thus generalizing...
The computation of symmetric functions can be tedious.
For this reason, the object of this paper is to devise a computer
program so that these symmetric functions can be handled automatically.
The contribution of this investigation is a heuristic for
finding the polynomials proved to exist by the Fundamental Theorem...
This paper is a classification of 181 problems, each of which involves the evaluation or application of determinants. The problems are those which have appeared in the "Problems and Solutions" sections of the American Mathematical Monthly, Deutsche Mathematiker-Vereinigung Jahresbricht, Mathematics Magazine, and School Science and Mathematics. The problems are classified,...
G. F. Drukarev has given a method for solving the Fredholm
equations which arise in the study of collisions between electrons
and atoms. He transforms the Fredholm equations into Volterra
equations plus finite algebraic systems. H. Brysk observes that
Drukarev's method applies generally to a Fredholm integral equation
(I-λ G)u...
This thesis has four main results. First we find a reduction form
for symmetric matrices over fields of characteristic two. This result
parallels the diagonalization theorem for symmetric matrices over
fields of characteristic not two.
Secondly we reduce our reduction form to a canonical form in
perfect fields of characteristic...
The paper concerns itself with the problem of heat transport
in a homogeneous, incompressible, isotropic, semi-infinite solid
whose boundary is nonstationary. The methods of solution in the one
dimensional case are discussed. Numerical examples and a method
for arriving at the solutions published by Bailey and Lakin in their
paper...
This paper is devoted to the study of families of tangent lines
to curves in Euclidean three dimensional space by the medium of a
particular representation for lines.
First, a ring of elements called dual numbers is described,
and a vector space over this ring, whose elements are called dual...
The objective of this paper is to describe the design of a real-time system to control two hydroelectric power plants by a digital
computer. The two controlling relations are stated as the continuity
of water flow and the inequality of power generation requirements.
It contains the logical sequence in finding...
As indicated by the title, this thesis generalizes the Main Inertia
Theorem of Ostrowski and Schneider [8]. The first three results
concern the formation of a polynomial function f(A, A*, H) so that
the existence of an hermitian H for which f(A, A*, H) is positive
definite is a necessary...
One answer to the problem of missing observations in two-way
classification experiments is to insert estimates of missing observations
into deficient cells. Once missing observations have been estimated,
the experimenter may proceed with his analysis using the
familiar normal equations which apply to complete data. This paper
discusses generally the...
The Cantor set is a compact, totally disconnected, perfect
subset of the real line. In this paper it is shown that two non-empty,
compact, totally disconnected, perfect metric spaces are homeomorphic.
Furthermore, a subset of the real line is homeomorphic
to the Cantor set if and only if it is...
This thesis treats the problem of enumerating equivalence
classes of Euler paths of full graphs. A full graph
is a complete, unordered, graph with no loops or repeated
edges. Two Euler paths are equivalent if and only if one
can be transformed into the other by a finite sequence of...
Properties of Mellin transforms are applied to the summation
of infinite series. A specific example of this application leads to the
establishment of certain properties of a generalization of Lerch's zeta
function.
Nine powerful methods of generating new tables of Mellin
transforms from existing tables of Mellin and other integral...
In his book on abstract algebra, Nathan Jacobson
poses and solves the problem of finding the number of
ways of inserting parentheses in a string of given length
with binary operators. We continue the work of Jacobson
and go beyond it in that we no longer consider one binary
operator...